Pith Number

pith:65CGWMIK

pith:2016:65CGWMIKUQRL4H436ENFAV2W3X

not attested not anchored not stored refs pending

Symmetry, Geometry, and Quantization with Hypercomplex Numbers

Vladimir V. Kisil

arxiv:1611.05650 v1 · 2016-11-17 · math-ph · math.CV · math.MP · math.RT · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{65CGWMIKUQRL4H436ENFAV2W3X}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:53:20.502993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7446b310aa422be1f9bf11a505756ddfb23d319d8b4f5c42c0f9615909f7418

Aliases

arxiv: 1611.05650 · arxiv_version: 1611.05650v1 · doi: 10.48550/arxiv.1611.05650 · pith_short_12: 65CGWMIKUQRL · pith_short_16: 65CGWMIKUQRL4H43 · pith_short_8: 65CGWMIK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/65CGWMIKUQRL4H436ENFAV2W3X \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f7446b310aa422be1f9bf11a505756ddfb23d319d8b4f5c42c0f9615909f7418

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cada41ef9d13ae6237ce6d5bf9dbfea4f2de8f2436895c86ffc5319de6122e2",
    "cross_cats_sorted": [
      "math.CV",
      "math.MP",
      "math.RT",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-11-17T12:15:52Z",
    "title_canon_sha256": "b2e3bf5c50ffb280d81fc977457ed4a2fecf815ed39a55d28e7b7da2d082344b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.05650",
    "kind": "arxiv",
    "version": 1
  }
}